1 Simulia Community Conference, Berlin, May 2015 Hydraulic Fracturing Simulation for Fracture Networks Stephan Arndt, Wouter van der Zee, Tobias Hoeink Baker Hughes Jianhu Nie formerly of Baker Hughes Abstract: The term ‘Unconventional Reservoirs’ is used in the oil and gas industry for hydrocarbon reservoirs that have very low permeability in the magnitude of microdarcy (μd) and therefore rely on artificially introducing pathways for fluids and gases, commonly by using hydraulic fracturing techniques, to enable economic production. This approach of using fracturing stimulation campaigns is also increasingly used to improve production in mature oil and gas fields. Industry estimates for North America indicate that more than half of all stimulation treatments have no impact on production, despite this technique having been in use in numerous onshore wells for more than a decade. Creating fractures connecting the source rocks to the well whilst allowing fluids to flow, either with new hydraulic fractures and/or activating existing natural fracture sets can have a large impact on production. Optimising the current approach based on determining its many parameters and adapting experience based knowledge to other regions in the world poses a complex challenge with the goal to understand and predict the effectiveness of the stimulation campaigns. Significant progress in the simulation of fluid driven crack propagation for a single fracture occurred with recent updates of Abaqus capabilities including coupled fracture and pore fluid flows with porous medium deformation. This paper looks at the challenges using different modelling approaches using Abaqus such as Cohesive Elements (COH), Extended Finite Element Method (XFEM), Smooth Particle Hydrodynamics (SPH) and coupled Eulerian Lagrangian methods (CEL) with the goal to extend applications to more complex geometries with interaction of multiple fractures and stress shadowing effects. Keywords: Cohesive Elements, Coupled Analysis, Coupled Lagrange Euler (CEL), Crack Propagation, Damage, DFN, Drilling, Fracture Initiation, Fracture Propagation, Geomechanics, Horizontal Wells, Pore Pressure, Poro-Elasticity, Reservoir, Smooth Particle Hydrodynamics (SPH), Wellbore, XFEM. 1. Introduction A large number of publications on the topic of ‘Unconventional Reservoirs’ are available and only a few key points are summarized here with the focus on Hydraulic Fracturing Simulation using Abaqus’ coupled pressure-deformation capabilities, including cohesive elements, extended finite element method and other techniques. For production from unconventional reservoirs, it is important to overcome the limitations in flow rates caused by the low permeability. One aspect is increasing the reservoir contact, i.e. the length
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Simulia Community Conference, Berlin, May 2015
Hydraulic Fracturing Simulation for Fracture Networks
Stephan Arndt, Wouter van der Zee, Tobias Hoeink
Baker Hughes
Jianhu Nie
formerly of Baker Hughes
Abstract: The term ‘Unconventional Reservoirs’ is used in the oil and gas industry for
hydrocarbon reservoirs that have very low permeability in the magnitude of microdarcy (μd) and
therefore rely on artificially introducing pathways for fluids and gases, commonly by using
hydraulic fracturing techniques, to enable economic production. This approach of using
fracturing stimulation campaigns is also increasingly used to improve production in mature oil
and gas fields. Industry estimates for North America indicate that more than half of all stimulation
treatments have no impact on production, despite this technique having been in use in numerous
onshore wells for more than a decade. Creating fractures connecting the source rocks to the well
whilst allowing fluids to flow, either with new hydraulic fractures and/or activating existing
natural fracture sets can have a large impact on production. Optimising the current approach
based on determining its many parameters and adapting experience based knowledge to other
regions in the world poses a complex challenge with the goal to understand and predict the
effectiveness of the stimulation campaigns. Significant progress in the simulation of fluid driven
crack propagation for a single fracture occurred with recent updates of Abaqus capabilities
including coupled fracture and pore fluid flows with porous medium deformation. This paper
looks at the challenges using different modelling approaches using Abaqus such as Cohesive
Elements (COH), Extended Finite Element Method (XFEM), Smooth Particle Hydrodynamics
(SPH) and coupled Eulerian Lagrangian methods (CEL) with the goal to extend applications to
more complex geometries with interaction of multiple fractures and stress shadowing effects.
Figure 5. Abaqus model with solid element mesh parallel plates and SPH particles seeded in the fluid domain.
Figure 6. Comparison of the predicted SPH flow velocity with analytical solution (height profile evolution over time, left, center velocity, right).
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Simulia Community Conference, Berlin, May 2015
Investigations confirming mesh refinement (or particle density) convergence of this method and
on the influence of artificial viscosity to control stable time increment size on shear viscosity were
performed as well. These findings and continuation questions are outside the scope of this paper
and will be published separately in the future.
4. Application of cohesive element hydraulic fracture simulation
Three examples were investigated that used the cohesive element approach, based on the
validation for both cohesive elements and XFEM to correctly describe fluid-filled fracture
propagation and success in modelling intersecting fractures.
4.1 2D Simulation with intersecting fractures
To test the simulation capabilities for intersecting fractures, a quasi 2D-model with square
geometry is constructed in CAE. Abaqus/CAE 6.14-1 does not support the 12-node displacement
and pore pressure three-dimensional cohesive element in the “Mesh” module. Meshing can be
performed by using the 8-node, three-dimensional cohesive element and subsequently editing the
element type. The optional offset parameter allows the automatic generation of the mid-surface
nodes (nodes 9-12) that contain only pore pressure degrees of freedom. This can be performed in
Abaqus/CAE via Model, Edit Keywords or separately editing the input file to modify the entry for
the element definition for type COH3D8 by changing the element type and specifying an offset
value:
*ELEMENT, TYPE=COH3D8P, OFFSET=offset
The mesh stack orientation should be defined in the “Mesh” module to ensure the cohesive
elements are inserted correctly.
This approach does not allow generating intersecting fractures. In this case, all connected elements
need to have common pore pressure nodes, which is not compatible with the underlying geometry
and requires either further editing or mesh generation via scripting. The independent constitutive
and geometric thicknesses of the elements would allow inserting zero thickness cohesive elements
at all element boundaries without distortion of the mesh.
For this example, a model is created by defining a single layer of C3D8P elements (regular mesh,
100m x 100m, 1m size) intersected by a narrow geometry domain of 0.01m to contain the
cohesive elements (COH3D8P) in the mid-planes. The center piece solid element is deleted and
one node for each side of the layer is created in the center to be used as common pore pressure
nodes on the four attached cohesive elements.
The parameters from validation cases in (Zielonka, 2014) are used in the simulations (Young’s
modulus E = 17 GPa, Poisson Ratio v = 0.2, Fluid viscosity μ = 1 cPoise). An initial open fracture
is defined on the left side, with the initial length chosen as 25% of the model dimensions, using
the keyword:
*INITIAL CONDITIONS, TYPE=INITIAL GAP
ElementSet
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Simulia Community Conference, Berlin, May 2015
Both pressure and inflow volume-controlled boundary conditions yield the same results, either
using:
*BOUNDARY
NodeSet, 8, 8, InjectionPressure
or
*CFLOW, AMPLITUDE=RampUp
NodeSet, , InjectionVolumeRate
Following an initial *GEOSTATIC step to ensure equilibrium of the initial conditions for stress and
pore pressure, a *SOILS, CONSOLIDATION analysis step is performed using the unsymmetric matrix
solver as required for this problem type. Changes in pore pressure can be large, so an adequate
choice of the convergence tolerances for pore pressure, defined using the UTOL parameter, is
necessary. The initial in plane stress is set to S11 = 15MPa, S11 = 10MPa and S33 = 10MPa. For the
second model, S11 and S33 are swapped, rotating the stress 90 degrees.
The fracture propagation for the two models is shown in the time sequence in Figure 7 using the
fracture aperture variable (PFOPEN) and a 500x displacement magnification.
The simulation demonstrates the expected behavior. Initial tests were performed with the injection
in the center and initial gaps defined for all four cohesive elements connected to the central pore
pressure nodes to confirm fracture propagation occurs only in the plane normal to the least
principal stress. In this example the possible fracture paths are limited to the cohesive element
regions, so in the scenario where the least principal stress is horizontal, a redirection of the fracture
propagation direction can only occur at the center of the model. At this stage the fracture does not
propagate further laterally.
An important observation in the sequence of pictures is the reduction of aperture of the horizontal
fracture as the fluid escapes into the vertical fracture and stress shadowing occurs. This very
realistic behavior has significant implications for real-life stimulation treatments, as proppant
transport inside the fluid is affected in rather complex ways and the proppant might choke the
fracture tip.
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Time SH = 15.0 MPa / SV = 10.0 MPa SH = 10.0 MPa / SV = 15.0 MPa
300 s
600 s
900 s
1200 s
Figure 7. Evolution of fluid injection showing fracture aperture (PFOPEN) for cohesive elements with displacement magnification of 500x.
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4.2 Validation against experimental data
Results in (Blanton, 1982) allow the validation against experimental data. Here, samples of
dimensions 30cm x 30cm have been fabricated using synthetic rock blocks (“hydrostone”) with
existing fractures embedded at different angles (90, 45,60) and subjected to different tri-axial
compressive stress states before fluid injection propagates a hydraulic fracture. Three of these
experiments, showing all three different observed interaction modes in the same model geometry,
were chosen for validation (Table 2).
Table 2. Validation experiments chosen from (Blanton, 1982)
Test Fracture
Angle SXX SZZ
Interaction Mode
CT-4 60 12.0 MPa 10.0 MPa Opening
CT-8 60 20.0 MPa 5.0 MPa Crossing
CT-21 60 14.0 MPa 5.0 MPa Arrest
As several parameters from the experiments, such as injection fluid pressure and hydrostone
strength (fracture toughness), are not provided in the paper because we follow the argumentation
in (Fu, 2012) to narrow the possible range according to observations from the tests. This also
allows for comparison with these and other numerical simulations using the same reference.
Contrary to the approach in (Fu, 2012), where crack propagation crossing the natural fracture is
not allowed and the stress intensity factor KI is evaluated instead, the Abaqus simulation allows
crossing through the natural fracture by extending the cohesive elements to the specimen
boundary.
An initial gap opening has to be specified in the model for the cohesive elements at which fluid
injection occurs as in the previous example. It would seem obvious to use the same approach to
create the natural fracture, but the element degradation of the shear stiffness changes the stress
equilibrium in the geostatic step significantly, especially in the case of high differential stress (CT-
8). The fracture toughness has no major influence on the fracture propagation; therefore, it is
sufficient to have the natural fracture closed both in the initial conditions and in equilibrium by
choosing a shear strength larger than the shear stress on the inclined plane. The presence of
cohesive elements subsequently allows the fracture to open.
A coarser regular mesh and a finer advancing front mesh with ~4000 and ~20,000 elements,
respectively, have been tested with similar results. A time sequence of the three cases is shown in
Figure 8, where the fine mesh is suppressed for better clarity. Displacements are magnified 100x.
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Time CT-4 (Opening)
12.0 MPa 10.0 MPa CT-8 (Crossing)
20.0 MPa 5.0 MPa CT-21 (Arrest)
14.0 MPa 5.0 MPa
0.30 s
0.45 s
0.60 s
0.75 s
Figure 8. Evolution of fluid injection showing gap flow volume rate (GFVR).
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Simulia Community Conference, Berlin, May 2015
As shown in the evolution of fracture gap flow volume rate, all three tests show the correct
fracture interaction mode. CT-21 does show minor fluid propagation along the natural fracture, but
this is small compared to the fluid volume and fracture opening on the other side of the injection
point. Again, higher confining stress shows a smaller crack opening in CT-4 as in the previous
example.
4.3 3D Simulation with parallel fractures
Current research into the interaction of different fracture stages, stress shadowing between parallel
fractures and alternative sequencing between adjacent parallel wells (‘Zipper Frac’) demonstrates
the significance of 3D simulation capabilities. (Bunger, 2014) and (Izadi, 2015) provide analyses
of the parameters for closely spaced fractures and a detailed analysis of the zipper frac concept
using a continuum damage approach with Abaqus is presented in (Shen, 2014).
The chosen test case for 3D simulation of parallel fractures with cohesive elements is the
simultaneous propagation of equally spaced fractures under the assumption of equal injection
pressure, neglecting wellbore hydraulics and perforation friction effects. A 3D model was built
using Abaqus/CAE, including the wellbore geometry (75/8 in diameter), a reservoir volume of 40m
vertical extent with cap rock above and basement below for a total height of 60m, five parallel
planes meshed with cohesive elements with 5m separation, and partitioning to allow for mesh
transition from the well. Lateral symmetry is used to reduce element numbers. No vertical
symmetry was used while building this model to allow for gravity and stress gradient effects
(although the case presented here does not include these effects). The model geometry and mesh
with ~100,000 elements are shown in Figure 9.
Figure 9. 3D model with horizontal well, reservoir volume, five planes containing cohesive elements for hydraulic fractures (left) and mesh discretization (right).
Using pressure boundary conditions as in the previous examples, volume flow and fracture
propagation occurs. Higher lateral stress and rock stiffness in the cap rock and basement provide
fracture containment inside the reservoir.
Unlike a simulation with a constant volume flow rate for each fracture, the constant pressure
generates flow rates affected by the stress changes. The inner fractures become restricted by the
presence of neighbors on both sides and fracture aperture and total volume are reduced
significantly as seen in Figure 10. This quantitative simulation experiment is consistent with
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published simulation results. Further work is required to quantify the effects above and validate
results against other available sources.
Figure 10. Evolution of fracture aperture in simultaneous parallel fractures.
Analysis times for this 3D problem are in the range of several hours using a single computer with
16 CPU cores, indicating that there is no immediate practical limitation for this simulation
approach.
5. Conclusions
The stated challenge for this paper is to extend applications to more complex geometries with
interaction of multiple fractures and stress shadowing effects. By choosing the cohesive element
approach in Abaqus/Standard it becomes possible to perform 3D hydraulic fracturing simulations
that satisfy the following criteria:
The analysis capability includes essential physical behaviors such as coupled pressure-
deformation (Poroelasticity), fracture propagation and fracture fluid flow with leak-off.
Validation of propagation of a single fluid-filled fracture against analytical solutions,
such as KGD geometry and Penny-shaped cracks, and mesh convergence have been
shown (Zielonka, 2014).
Successful validation of 2D fracture interaction observed in experiments. Different
interactions modes such as fracture diversion (or opening), crossing a natural fracture,
and arrest are predicted correctly.
The implementation of intersecting cohesive elements used in the 2D examples can be
extended to include all element boundaries in the model in 3D, providing a general 3D
simulation capability.
Interaction of parallel fractures in 3D simulations and qualitatively correct behaviors as
stress-shadowing-limiting fracture apertures, as shown in simulations using other codes,
is observed.
Acceptable performance and time incrementation for large 3D problems is demonstrated,
combined with scalability using the parallel solver.
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Simulia Community Conference, Berlin, May 2015
A major limitation lies in the necessary choice of either using cohesive elements or XFEM.
Cohesive elements placed at solid element boundaries limit the possible fracture path to element
boundaries and XFEM does not support intersecting fractures or nucleating new fractures.
These are common challenges in the focus on coupled 3D hydraulic fracturing simulation
capabilities for the oil and gas industry in recent years and the desire to include more effects will
drive further developments. With the approach shown in this paper Abaqus in its current release
can be used to increase understanding of interaction of fractures in stimulation campaigns and to
help reduce expensive trial-and-error approaches.
6. References
1. Abaqus Benchmarks Guide, version 6.14-1, Providence, RI, USA, 2014.
2. Abaqus Example Problems Guide, version 6.14-1, Providence, RI, USA, 2014.
3. Arndt, S., Beck, D., Reusch, F., Thin, I., Stone, C., Heap, M. & Tyler, D. “Deep and High
Stress Mining – Deformation and Seismicity”, In Proceedings of Abaqus International Users’
Conference. Paris, France. May 22-24, 2007.
4. Arndt, S., Beck, D. & Reusch, F., “Modelling of Large Open Pit Stability Using ABAQUS”,
In Proceedings of Abaqus International Users’ Conference. Paris, France. May 22-24, 2007.
5. Arndt, S., “Advances in Mining Simulations”, In Proceedings of Simulia Customer
Conference. London, England. May 18-21, 2009.
6. Arndt, S., Fillery, B., “The Importance of Simulation in Geotechnical and Mining
Applications”, In Proceedings of Simulia Customer Conference. Barcelona, Spain. May 17-
19, 2011.
7. Beck, D., Fillery, B., & Reusch, F., “3D Hydro-mechanical Simulation of Faulted Open Pit
Slopes”, 44th U.S. Rock Mechanics Symposium and 5th U.S.-Canada Rock Mechanics
Symposium, 27-30 June, Salt Lake City, Utah, 2010.
8. Blanton TL. An experimental study of interaction between hydraulically induced and pre-
existing fractures. Proceedings of SPE Unconventional Gas Recovery Symposium. Pittsburgh,
Pennsylvania. Society of Petroleum Engineers, 1982; 559–571. DOI: 10.2118/10847-MS.
9. Brown, T., “Deep Mining 2012 - Y. Potvin (ed)”, Australian Centre for Geomechanics, Perth,
ISBN 978‐0‐9806154‐8‐7, Perth, 2012.
10. Bunger, A.P., Peirce, A.. Numerical simulation of simultaneous growth of multiple interacting
hydraulic fractures from horizontal wells. In ASCE Shale Energy Engineering Conference,
Pittsburgh, PA, July 21–23 2014. ASCE.
11. Economides, M.J, Hill, A.D., Ehlig-Economides, C., Zhu, D., “Petroleum Production